Questions tagged [heap-sort]
The heap-sort tag has no usage guidance.
19
questions
1
vote
1answer
25 views
How to solve this summation of ceiling function in BUILD-MAX-HEAP algorithm
I am stuck on solving this problem and cannot understand how is the ceiling function omitted or solved.
Please help.
The equation:
$\sum_{h=0}^{\lfloor\lg n\rfloor} \lceil\frac{n}{2^{h+1}}\rceil O(h)...
1
vote
1answer
50 views
Max heap and array relation
This question is about max heap and array
Suppose there is max heap $h$, with $n$ data items already stored in $h$. An array that is formed by inserting a value larger than all the values in $h$ at ...
0
votes
2answers
167 views
is AVL tree is better than heap for sorting purpose?
for sorting n elements what is better to use AVL tree or heap data structure and why? Can someone explain in brief?
0
votes
1answer
198 views
Show that,with the array representation for sorting an n-element heap, the leaves are the nodes indexed by n⌊n/2⌋+1,⌊n/2⌋+2,…,n
The Question of the CLRS $6.1-7$ exercise reads as:
Show that, with the array representation for sorting an n-element heap, the leaves are the nodes indexed by $\lfloor n / 2 \rfloor + 1, \...
0
votes
1answer
57 views
Please provide me a solution of Max-Heapify using Recursion Tree
I tried my best to solve the recurrence relation.
$T(n) \le T(2n/3) + \Theta(1)$
Using the recursion tree.
I could reach out the boundary condition when at depth ...
3
votes
1answer
51 views
Are comparison sort algos appropriate for SUBJECTIVE sorting?
I've been tasked with creating an online feature that ranks 50 fantasy characters from a variety of domains based on combat acumen and polls users one which one is the most powerful based on their ...
0
votes
2answers
1k views
Worst case time complexity of heap sort
I was learning about heaps, and came to know that the worst case time complexity of heap sort is Ω(n lg n). I am having a hard time grasping this. My reasoning is as follows:
...
0
votes
0answers
1k views
Find K largest elements using a priority queue [duplicate]
Say we have a Priority Queue of size 1000 that is implemented using Max Heap.
Now if i want to get the top 5 elements, the most laid back method is to poll the maximum 5 times, resulting in a set of ...
3
votes
0answers
711 views
How to determine the fewest number of comparisons for Heapsort?
I'm currently doing an exercise that asks to prove that Standard-Heapsort requires at fewest $\frac{1}{8} n \log(n) - O(n)$ comparisons, in its best case.
In its average case, Heapsort only requires $...
0
votes
1answer
727 views
Why is Heapsort in O(n log n) if not all n operations take time log n?
let's consider that we already have constructed heap array.
so from this, when we do heap sort, the number of elements that have to be sorted decreased. I mean heap decrease.(which also means heap ...
0
votes
0answers
525 views
How to build a heap better than Incremental and In-place method using decision tree?
For an array A = [a1, a2, a3, a4] of distinct numbers, I have built heap using binary decision tree by Incremental and In-place method.
Incremental method:
In-place method:
Is there a way to build ...
0
votes
2answers
770 views
Heap sort best case time - $\mathcal O(n)$?
It is given $\mathcal O(n\log n)$ everywhere but in best case it should be $\mathcal O(n)$, isnt it ?
The argument here is, If my input has all the same keys, then every time I delete the root, I do ...
4
votes
2answers
188 views
If a min heap of [n] is stored into an array, what are the minimum and maximum values for an element at a given index?
If we store a min heap of $n$ elements, $\color{Blue}{[1,2, \dots n]}$ into an array, then what can be minimum value present at any index $i$ and maximum value present at any index $i$. (elements are ...
0
votes
0answers
73 views
Analysis on comparisons in a heap-like sorting algorithm
I've stumbled a heap-like sorting algorithm on the Internet as followed:
$\\$
For convenience, given a list of $2^n \; (n \in \mathbb{N^*})$ distinct numbers to be sorted increasingly.
Step 1: From ...
0
votes
1answer
830 views
When the heapsort worst case occurs?
The best-, average-, and worst case time complexity of Heapsort for $n$ distinct keys are all $\Theta(n \lg n)$.
What are the worst-case inputs for heapsort?
1
vote
1answer
437 views
Does Heapsort work in time o(n log n) in the best case?
Is it possible for Heapsort to work in time $o(n\log n)$ on certain inputs?
For example in case of Insertion sort it is possible, however when it comes to Quickssort it is not possible. What about ...
1
vote
0answers
163 views
Minimum exchanges for heap sort
I'm studying heap sort and was presented with the following question.
What is the minimum number of items that must be exchanged during a remove the maximum operation in a heap of size N? Give a ...
1
vote
1answer
606 views
Lower bound on distinct element heapsort
I've been self-studying algorithms and am currently working on one of the starred exercises from CLRS:
Exercise 6.4-5
Show that when all elements are distinct, the best-case running time of heapsort ...
0
votes
1answer
2k views
Build-Max-Heap vs. HeapSort
I'm not sure whether my definition for these 2 terms are correct. Hence, could you help me verify that:
HeapSort: A procedure which sorts an array in place.
Build-Max-Heap: A procedure which runs in ...
